Chaotic or Not?

Consider the dynamical system generated by the discrete recurrence

z n + 1 = f ( z n ) = 2 z n . z_{n+1} = f(z_n) = 2z_n.

Is this system chaotic ?

Yes No Maybe

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2 solutions

Matt DeCross
Apr 25, 2016

Relevant wiki: Chaos Theory

This dynamical system does not satisfy the topological mixing criterion for a system to be chaotic. Given a set of nearby adjacent initial conditions, the asymptotic behavior is predictable: the points diverge at an quadratic rate so that the difference grows by a factor of two each recursion. This corresponds to a confinement of trajectories in phase space; the phase portrait is quite boring!

Luigi Lamacchia
Apr 27, 2016

This seems to be a simple parabol y=x^2

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